It had been feared that the 29-year-old would miss the remainder of the season with the knee ligament injury that he suffered last year.
However, having undergone an operation and returned to light training, Bowe has claimed that he could be available for selection again at some point next month.
"The knee is coming along well. Hopefully, I'll be back within the next four or five weeks," said Bowe. "I'm 12 weeks post operation at this stage and it's meant to be a 16-week recovery period."
It has been reported that Ulster's Heineken Cup quarter-final against Saracens on Saturday, April 6 will come too soon for Bowe.